Question

If charge \(+q\) is taken from one point to another over an equipotential surface, then

• A. work done on the charge continuously increases.
• B. work is done by the charge.
• C. work done on the charge is constant.
• D. no work is done.

Hint:

Work done equals charge times potential difference, which is zero on an equipotential surface.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
The work done in moving a charge between two points is \(W=q(V_B-V_A)\), where \(V\) is the electric potential.

Step 2: Equipotential surface
All points on an equipotential surface are at the same potential. So \(V_B-V_A=0\) for any two points on it.

Step 3: Calculation
\[ W=q\times0=0 \]

Step 4: Check the options
(A) and (C) say work is done, which is not so. (B) says the charge does work, which is also not so. The electric force is always perpendicular to the surface, so it has no component along the displacement. No work is done, option (D).

Final Answer:
The potential difference is zero on an equipotential surface, so no work is done, option (D). \[ \boxed{\text{No work is done}} \]